how to measure the size of the earth - uzh
TRANSCRIPT
Boris Pestoni, Vytenis ŠumskasUniversity of Zürich
AST 202 The Universe: Contents, Origin, Evolution and FutureMarch 8, 2016
Aristotle agreed
Arguments:� Shadow is round during lunar eclipses;� Compression and convergence;� Travellers.
Aristotle (384 – 322 B.C.)
The first success!
Eratosthenes (276 – 195 B.C.)A prezi about his experiment:
https://prezi.com/d3kf13_gvvri/untitled-prezi/
Willebrord Snell(1580 – 1626)� Chain of 33 triangles
between two cities in the Netherlands
� Radius R = 6368,7 km
Giovanni Cassini (1625 – 1712)
� Two measurements, in north and southof France, using triangulation method: two different resultsÎ Earth is an ellipsoidand not a sphere
In which direction is the Earth flattened?� Cassini: from the
previously mentionedmeasurements, the ellipsoid is elongated in the polar regions
� Newton: as a results of the superposition of the gravitational and centrifugal forces, the ellipsoid is flattened in the polar regions.
Prolate or oblate ellipsoid?� Two expeditions, one in Peru and the
other in Lapland.� Purpose: measure the length of a
meridional degree. If the 1° meridionalarc in Lapland were shorter than that in Peru, Cassini would be right.
� Result: the meridional degree ofLapland was longer Î Newtonwas right.
Measurements of the new parameters� To measure: 1. equatorial radius a;2. polar radius b;3. flattening f = (a-b)/a or inverse
flattening I = 1/fTwo examples:
Reference ellipsoid name
a (m) b (m) I
Maupertuis (1738) 6397300 6363806,283 191IERS (2003) 6378136,6 6356751,9 298,25642
Limits of measurements, satellites� Molodenskii (1945): it is impossible to
determine the geoid only from measurementscarried from the surface of the Earth.
� Nowadays: satellites, GPS
Summary
Spherical Earth
Pythagoras and Aristotle: the shape of the Earth is a sphere
Eratosthenes: R = 5936 kmAl Biruni: R = 6356,7 km
Snell: R = 6368,7 km
Ellipsoidal Earth
Cassini: the shape of the Earth is an ellipsoidNewton: the ellipsoid is flattened in the polar regions
Maupertuis: a = 6397300 m, b = 6363806, 283 mIERS: a = 6378136,6 m, b = 6356751,9 m
Geodesic Earth Gauss: the shape of the Earth is a geoid that differsin different ways from the mathematical shape
Main reference: Oldrich Novotný, Motion, gravity field and figure of the Earth, Universidade federal da Bahia, Salvador de Bahia, 1998